In such a method known from the DE 39 31 110 C2, the twisting stops are formed by two stationarily arranged delivery mechanisms, of which one is arranged upstream of the false twisting unit or units, and the other one downstream of the fixing unit, which is designed either as a heating device or as an air-circulating device. The alternating formation of the S- and Z-twists is carried out in a predetermined cycle by switching on and off the clamping action of the false twisting unit. Since, however, the second twisting stop is arranged downstream of the fixing unit in yarn advancing direction, the S- and Z-twists earlier applied to the yarn are, depending on the twisting direction, partially again untwisted and partially yet more tightly twisted in the yarn section extending downstream of the false twisting unit. Thus it is not possible in this manner to produce a yarn which has reproducible alternately defined S- and Z-twists. Furthermore nontwisted sections with a lesser S- or Z-twist are each created between the sections with S-twist and the sections with Z-twist.